View Full Version : Parabolic curves for solar collectors/hot dog cookers

03-05-2001, 10:05 PM
Do any of you mathematician/solar energy guru's out there have a dxf or ? file of a true parabolic curve that is copyright free so the rest of us can make hot dog cookers or solar water heater parts? tnx in advance ko

Gerald D
03-06-2001, 04:50 AM
How to construct your own parabolic curve for your cooker:

1. Decide how far you you want the focal point (F) to be away from the reflector directly behind it (R)
2. Draw a baseline (B) that is 2 times FR away from the focal point. Therefore BF = 2 X FR, or put in another way, the reflector is halfway between the focal point and the baseline.

(This is the most convenient (for reflectors) definition of a parabola: THE REFLECTOR IS THE SAME DISTANCE FROM THE FOCAL POINT AS IT IS FROM THE BASELINE)

3. Now draw a construction line (C) parallel to the baseline, but at a distance (towards F) of slightly more than the original BR. Letís call this distance BC.
4. Draw a circle with radius BC around the focal point. Note that it is BC, not FC, although the centre is on F.
5. The parallel construction line and the circle will intersect at two points that are on the parabola.
6. Carry on with a couple more constuction lines and circles, each time finding the intersections when the parallel distance equals the radius.

I am not going to get involved with a discussion on drawing a curve throught the points and how the ShopBot will give a true resolution Ė it has been discussed elsewhere on this forum from time to time. However, for cookers, short straight lines are probably OK.


03-06-2001, 05:13 PM
now here is an interesting project !

With my 3d-CAD one can place a curve/arc/parabolic
and then spin it to get either a solid or surface.
Given GD's formula(s) one could construct the curve with points and then pass a b-spline thru them to get the size/scale desired also.
It'll depend on the parabolic function capabilities of whatever CAD you use.

Of course the toolpath to dig out the whole thing is the real problem.

One "could" pass sets of parallel "cutting planes " thru the parabolic surface to get the "top view" circles. And once those circles are defined, then do a "copy parallel" of the circles, inward, to get concentric "cutting circles.

A bit labor intensive but you would have the opportunity to select ...
1. plane seperation to suit tool size
2. Circle offset to suite tool size

Final pass would then just be the original circles.

As you can see I'm always attempting ot get CAD to create the toolpaths without having to employ an expensive and usually expensive post processing package/"add on" to the CAD.

Given success on the CAD function ...
I'm not sure how you will be "surfacing" the final cut and finished part to achieve reflectivity an heat dissapation.

I have heard that "fluid/liquid" when SPUN will create a parabolic shape.
So, maybe one could spin a puddle of thin epoxy or other curable fluid until it hardens and THEN do some sort of reflective coating.

This is gonna take some effort so I wouldnt run out and buy those HotDogs just yet :-)

03-06-2001, 07:15 PM
I'd always heard that spinning a fluid makes a mess.

Gerald D
03-07-2001, 12:16 AM
Bob, I can see you salivating already!

Shouldn't a 2D parabola be sufficient for the sausage of a burger - maybe even better!. The sausage is a a thin cylinder which can pass through the focal point perpendicular to the sketch above.

If you cut two plywood supports to fit in between the baseline and the reflector, space them one hotdog length apart, and put a sheet of shiny stuff on the curved surface, you could be cooking in about an hour if the sun is shining!

Another useless statistic that is cluttering my mind: The sun's radiation is about a kilowatt per square yard (on a surface perpendicular to the rays, here on earth, if no clouds/pollution in the way, if sun has risen to a reasonable height, etc. etc.)

03-07-2001, 07:57 AM
You'll need a decent speed control for the fluid spinning "trick".

BTW, I've sworn OFF hotdogs !

I'm WITH YOU but lets not loose track of the original problem posed by KO.

Certainly PLANAR parabolas are easier to construct. Like back in highschool with a band saw, when we still remembered some algebra :-)

Obviously we SB users will NOT be doing mass production of Parabolic cookers. Therefore the easiest thing to do is to head for the nearest military scrap yard and buy a "used" antenna.

03-07-2001, 09:51 AM
Here's a little something to play with.


It is set up to demonstrate the Swept curve pocket in Vector 9.0. There is an Excel spread sheet with formulae included that you can use to play with the parabolic shape. If you do not have version 9.0, you could copy-paste the offset-spline curve about the Z axis with multiple copies to create an Orange section type of cut or use the Skin function to create passes in a radial direction.

It should be obvious from the graphics that it is quite easy to develop the "waterline" tool path with Vector 9.0. We also have put some pictures of parts cut with this function on the Vectorcam web site.

Gerald D
03-07-2001, 10:24 AM
Bob, that is one of the things that I envy the most about you Americans - the quality of stock, and the convenience, of the "nearest military scrap yard"!

03-07-2001, 12:01 PM
Fred is definately on the right track !
I like his web example.

He's done what I would have with my CAD's curve and surfacing functions.

But we still dont have a tool path,... do we ?
I havent gotten into Vector usage.

Unless Vector does a nice bunch of concentric, circular toolpath "THINGS" then it's not much use, except for the drawing and conceptulization ( like my CAD too ).
I'm not taking a shot here. ok :-)
Vector looks like it has some kewel functions.

I'm just back to my original notion of passing planes thru the parabolic surface that Fred or whoever has created to help generate the toolpath(S).

Gerald, yep ! we DO have lotsa scrap !
if we havent ground it all up and used it as aggregate in some new project.
But seriously folks, the last time I was actually at a military scrap yard was 25 yrs ago.

Hey, wait a minute ...
isnt the JUNK YARD WARS cable tv program originating from the UK ???

03-07-2001, 12:47 PM
It's a tool path, compensated for a 1 inch diameter full radius cutter. (I put photos of some wooden parts that I cut on the Vector 9 page. Note: they are not round)

You can generate a planar slice by breaking the swept curve into sections the thickness of your material(copy-paste a line in X-Z plane, multiple copies and break intersect) and then generating the rings. Each one can be a separate tool path & they can all be arranged on a flat sheet with locating/alignment holes so that it is easy to stack them up and glue together the complete assembly from sheet stock.

I'm considering making this a class project for our next Shopbot-Vector training class.

03-07-2001, 06:59 PM
I have seen the tool path for the parabole on the Vector site,
I do not understand how you rough the shape before finishing it.
Is the cutter suposed to cut the shape in one go ?

Olivier .

03-07-2001, 09:44 PM
I think Gerald is on the right track, a couple of frames with a parabolic curve and shinny stuff. A round parabolic dish would be perfect for super heating the end of the hot dog. It seems a less than perfect long curve would end up heating the whole thing. Probably find just what you need in something like "Mother Earth News".

03-08-2001, 08:31 AM
Olivier - Vector has a built in function for making roughing passes for 3D contours. It is called Contour Tooling (I call it copy contour). The function works very much like the pocketing function, in that you specify depth of cut per pass and total depth to be cut. It automatically makes multiple copies of the contour and connects them together. You may need to combine it with the Cut above Z function to remove air cuts. I had actually conceived of making the dish in slices from MDF or particle board. Something like the way that Millit processes a 3D model.

In Version 9 of Vector, there is also a new pocket function that will directly develop roughing passes in 3D from the finish passes created with the X-Z profile, swept toolpaths. This one does not copy the profile to rough out the pocket, but rather makes Z depth planar passes, within the constraints of the pocket. It properly handles submerged islands, so that you could design a standoff in the center to place the food on.

J.Jorgensen - The contour developed with the PLC spreadsheet on our web page could as easily be rotated flat & become 1/2 of a parabolic frame cut from sheet stock. By selecting just the curve of the spline, and Special - Verify, you could also develop the length of the material that you would attach to the frame. I would think that cardboard with aluminum foil would make an excellent reflector for cooking purposes. Not as durable as steel or plastic, but good enough for a prototype. ;-)

03-08-2001, 10:00 AM
I have created a small tutorial in html to
explain my ideas for parabolic creation and
cutting from a single block of "Whatever". ie foam


Be patient, I used lots of screen captures !

I probably wont ever actually DO this parabola THANG, but it was a FUN exercise.

Fred will have to assist with discovering Vector
functions that match ( or best ) the functions
that I used in my MicroStation 3D-CAD.

03-08-2001, 04:16 PM
Hi Fred,

I'm running Netscape 4.76 and get nothing when I follow the spreadsheet link.

03-08-2001, 06:33 PM
Fred...where do we find your posted pics?
My vector site at centriforce.net doesn't even mention Vector 9? Could you please give those of us who are interested a link?

03-08-2001, 07:04 PM
http://www.vectorcam.com or http://www.imsrv.com

Steve, you will need to have MS excel to use the spreadsheet file. Right click the link and save it to disk.

03-10-2001, 09:50 PM
Actually I can't stand hotdogs personally but the parabolic idea I gleaned from MotherEarth News years ago. Think that copy is still in the spare room. 5 yrs ago I made the cooker from their layout the old fashioned way "sabersaw" It looked kinda like half a 55 gallon drum with 3/4 ply ribs, cardbord skin lined with alum foil and got hot enough to burn your hand when passed thru the focal plane. If instead of a skewer, a water line was run at the focal plane, and a few or more hooked up in series etc. etc. hot tub heaters, hot water preheaters, steam generators?? Anybody out there know anything about stirling engines? Solar powered shopbots? Thanks for the input folks ko

03-10-2001, 09:53 PM
Forgot to ask. Question still applies. Does anyone out there have a DXF or ? of a parabolic curve? tnx ko

Gerald D
03-11-2001, 01:18 AM
Thought your question was fully answered above?? If you want dxf, this means to me that you want to import it into a CAD program for scaling. If you have CAD then you simply draw your own parabola, there is no rocket science involved. Maybe we got carried away (and how!), but drawing the parabola is really the simplest part of the whole exercise. (For my sketch, I actually had it on CAD, but didn't really think to keep and e-mail the file - sorry)

03-11-2001, 08:49 AM
Ken, a few years ago I got to the point of running my computer/control box off of the Heart 1200 watt (10 amps rated..)DC/AC inverter I use to convert power from the solar panel on my garage. The limitation then was that my PC router drew too much power at startup, and the Heart coudn't seem to handle the load.Since then the Trace company has come out with much larger inverters that produce pure sine wave power as well. I have moved from the garage to a shop , and haven't played with it any more, but I know the technology is capable. Trace can handle 4,000 wats easily, and a lot of people run their households with it..

03-11-2001, 07:29 PM
Darn trees. I didn't the forest again. thank you Fred ko